A novel scheme to insert carrier pilot to Gaussian Minimum Shift Keying (GMSK) signal using Binary Block Code (BBC) and a highpass filter in baseband is proposed. This allows the signal to be coherently demodulated even in a fast Rayleigh fading environment. As an illustrative example, the scheme is applied to a 16 kb/s GMSK signal, and its performance over a fast Rayleigh fading channel is investigated using computer simulation. This modem's 'irreducible error rate' is found to be Pe = 5.5 x 10(exp -5) which is more than that of differential detection. The modem's performance in Rician fading channel is currently under investigation

Feher, Kamilo

Leung, Patrick S. K.

English

NASA Technical Reports Server

N92-24170
A Novel Scheme to Aid Coherent
Detection of GMSK Signals in Fast
Rayleigh Fading Channels
Patrick S.K. Leung*, Kamilo Feher
Digital Communications Research Laboratory
Department of Electrical Engineering and Computer Science
University of California, Davis
Davis, CA 95616, U.S.A.
Abstract.
A novel scheme to insert carrier
pilot to GMSK signal using
Binary Block Code (BBC) and a
highpass filter in baseband is
proposed. This allows the signal
to be coherently demodulated
even in a fast Rayleigh fading
environment. As an illustrative
example, the scheme is applied
to a 16 kb/s GMSK signal, and
its performance over a fast
Rayleigh fading channel is
investigated using computer
simulation. This modem's
"irreducible error _ate" is
found to be Pe=5.5*10 -_ which is
more than one order of magnitude
lower than that of differential
detection. The modem's
performance in Rician fading
channel is currently under
investigation.
A limiting factor in relatively
low bit rate modem operation
over fast Rayleigh fading
channel is the "irreducible
error rate". In coherent
detection, this is caused by
the deep fades that force the
carrier recovery loop to hang up
and lose synchronization even in
the absence of channel noise
[14]. In differential detection,
it is caused by random FM noise
that partially destroys the
carrier phase coherency in
adjacent symbol time.
Theoretical and simulation
studies [4]' show that the
irreducible error rate for a 16
kb/s GMSK system with BT=0.25
and 2T differential detection is
approximately 10 -3 when the
Doppler frequency is fD=100Hz
[4].
1. Introduction.
GMSK [i] is a digital modulation
with appealing characteristics
for mobile communications. In
slow fading channels, GMSK can
be detected either coherently or
non-coherently. In a fast fading
channel environment however,
accurate carrier recovery is
difficult and non-coherent
detection is preferred [15].
* On leave from Dept. of Electr-
ical Engineering, Footscray Ins-
titute of Technology, Melbourne,
Victoria, Australia.
A useful technique to lower the
"irreducible error rate" is to
transmit an in-band pilot tone
at the carrier frequency.
Provided that mutual interfer-
ence with the data signal is
avoided, the received pilot can
be extracted using a simple
bandpass filter to aid accurate
coherent demodulation. The main
drawbacks of pilot schemes are
(i) the pilot takes up
additional power and/or band-
width, and (2) it destroys the
otherwise constant envelope
property of certain modulations.
However, under some
International Mobile Satellite Conference, Ottawa, 1990
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circumstances, the benefit of
coherent detection can outweigh
these shortcomings. Some well-
known examples are the Tone
Calibrated Technique (TCT) [5]
and the Transparent-Tone-In-Band
(TTIB) technique [6].
In the literature, there are
reports on in-band carrier pilot
insertion for linear modulations
such as BPSK [7] ,MPSK[8],
QPRS[9], and QAM[10]. But there
appears to be little study on
it's application to non-linear
modulation. In this paper, we
address the issue by extending
the technique to GMSK. We
propose a modified modem
structure which allows a carrier
pilot to be transmitted with
GMSK signal in band. Our study
demonstrates that for a given
application over fast Rayleigh
fading channel, the modem's
irreducible error rate is
reduced to Pe=5.5*10 -5 which is
more than one order of magitude
lower than that of differential
detection.
2. BBC coded GMSK modem with in-
band pilot.
GMSK is traditionally viewed as
a nonlinear digital FM signal
with Gaussian pre-modulation
lowpass filtering (see Fig. i).
TTIB is a well-known carrier
pilot insertion scheme with
potential application to GMSK,
however, its sophistication may
not be warranted in some
applications. The TCT technique
is more straightforward, but it
is not immediately obvious how
the technique can be applied to
non-linear modulations.
Fortunately, Laurent [12]
described a method that allows
some digital phase modulations
to be constructed by superposit-
ion of amplitude modulated
pulses p(t) in quadrature. In
this paper, we apply Laurent's
method to GMSK, and construct
the signal as an offset
quadrature amplitude modulation.
This alternative view of GMSK
suggests a convenient way to
insert an in-band carrier pilot.
We accomplish this by applying
BBC line code and highpass
filtering to the I/Q channel
data for the creation of a
spectral void zone at the
carrier frequency.
The block diagram of the
proposed modem is shown in
Fig.3. The binary input data
{bk} is split into I and Q
channel streams with the latter
delayed by Ts/2. Ts=2T(M-I)/M
where T is the input data bit
duration. The I/Q channel data
are convolved with the signaling
pulse p(t) before mixing with
the quadrature carriers to form
the GMSK signal. The waveforms
p(t) corresponding to several BT
values are shown in Figure 2.
They are smooth functions with
limited time duration, and their
pulse width decreases with
increasing BT value. In the
limiting case where BT approach
infinity, p(t) becomes a sine
pulse that corresponds to MSK.
To facilitate carrier pilot
insertion, both I/Q channel data
are encoded by the Binary Block
Code (BBC) [13] coder. BBC
suppresses the signal's low
frequency spectral component by
restraining its running digital
sum to be within bound. This
code has simple codec struc-
ture, and low redundancy
requirement. Its power spectrum
Su(f;t ) is given by [13]:
(sin(Mo)T/2) _2 .
TS,,( .f ; T ) = 1 "[M sin(o_T/2)J F((eT ; M ),
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International Mobile Satellite Conference, Ottawa, 1990
088
F(OOT" M ) = 0.645COS(MooT)- _ cos (2MooT)
COS(2Mo)T)- 0.2 1
" 0'85cos(2MooT) - 216 " 13 + 12COS(2MOOT)
x[-_[-7.2+6.4Cos(MOOT)-10.Scos(2Mo)T)+0.6cos(3MOOT)]
+ 0.05 [12cos(4MooT)+2cos(5MooT)+18cos(6McoT)+3cos(7M(-°T)]]
M odd and cotsfrequency in rad/s.
Figure 4 shows Su(f;t ) for M=3,7
and ii where _/(M-I) is the
code's redundancy. In this
study, the BBC code with M=II is
used. While it has a reasonable
spectral gap (see Fig 4), this
code only requires a i0 %
redundancy. The highpass filter
(with cutoff frequency fH Hz)
further limits the interaction
between data and carrier pilot
signal.
The received signal S(t) is
filtered by the receive BPF with
bandwidth equal to the bit-rate.
The carrier pilot is recovered
by the pilot BPF whose bandwidth
fB is set to be fB=fH . After
appropriate conditioning, the
recovered pilot coherently
demodulates the received signal.
3. Performance in fast Rayleigh
fading channel.
As an illustrative example, the
performance of a 16kb/s GMSK
modem with BT=0.25 and M=II BBC
coding in a fast Rayleigh fading
environment is studied using
computer simulation. The
Rayleigh fading process is
generated using the model
described in [2].
(a) Power spectrum considera-
tions.
Figure 5a. shows the normalized
spectrum of the transmit signal
where the carrier pilot power
level is i0 dB below the data
signal. Here fc is the carrier
frequency and fs=i/Ts. This
spectrum features a spectral
void zone of 800 Hz that has
been craved out by the fH=4OOHz
ideal HPF and M=II BBC coder.
Figure 5b shows the spectrum of
the same signal when fast
Rayleigh fading with Doppler
frequency fD = I00 Hz is
introduced. Both the pilot and
data signal are seen to suffer
spectral spreading as a result
of fast fading. In this case
though, the carrier pilot is
still distinguishable from data
signal, and it can be recovered
with a suitable bandpass filter.
Figure 5c shows the spectrum
when the spectral void zone is
only 400 Hz. Here, the carrier
pilot merges with the data
signal and carrier recovery
would be difficult.
(b) BER Performance.
BER performance of the modem in
a fast Rayleigh fading environ-
ment with fD = i00 Hz is shown
in Figure 6. Curve (a) plots the
performance when the pilot BPF
bandwidth is fB=300 Hz. Curve
(b) shows the performance with
fB=400 Hz. The two curves
crossover at approximately C/N =
28dB. Below this crossover
point, the modem with fB=400 Hz
has a slightly inferior
performance. But above the
crossover, the system with
fB=400HZ clearly performs
better. This behavior can be
explained as followed. When C/N
is small, channel noise
dominates the contributions to
the phase jitter in the
recovered pilot. The modem with
fB=400Hz admits more noise and
hence causes more error.
However, when C/N is large, the
modem performance is largely
determined by how accurately the
recovered pilot tracks the
channel fading characteristics.
Here, the fB=400Hz BPF recovers
more completely the fading
pilot's spectral contents, and
International Mobile Satellite Conference, Oflawa, t990
607
it brings about a lower bit
error rate and a lo_er error
floor (Pe=5.5*10 -_ Vs.
Pe=2.9,i0-4). Of course, one
needs to exercise caution in
employing too large a pilot
recovery BPF bandwidth. Firstly,
it admits more noise, but more
importantly, it demands a higher
cutoff frequency in the HPF of
the transmitter. This introduces
more ISI and performance
degradation.
For comparison, we also plot the
performance of a BT=0.25 GMSK
modem with 2T differential
detection as curve (c). The
Doppler frequency is the same at
fD = i00 Hz. Comparison between
curves (b) and (c) demonstrates
the advantage of pilot-aided
coherent demodula-tlon. For
small C/N (<20dB), the coherent
modem is about 2 dB better than
differential detection. But more
importantly, the coherent modem_
as an error floor of Pe=5.5*10
which is more than one order
of magnitude below that of the
differenti_l detection at
Pe=l.5,10 -_.
Figure 7 plots the modem's error
floor against the pilot recovery
BPF's bandwidth fB, with fD=100
Hz. The error floor is found to
be a concave function, and it
reaches its minimum at fB=400HZ.
(c) Effect of channel nonlinear-
its.
Figure 8 shows the effect of
channel nonlinearity on the
signal spectrum in a fast
Rayleigh fading environment. The
nonlinear characteristics is:
so (t) =si (t)/(i+0- 414" Isi (t) I)
where si(t) and so(t) are the
input and output signal
respectively [ii]. The Doppler
frequency is fD=100Hz and
fB=400HZ. Comparison with Fig.5b
iSdicates the presence of
further spectral spreading. This
is caused by the non-constant
signal envelope resulting from
the inserted pilot. However, the
degree of spreading in this case
is only minor.
4. Conclusion.
A scheme to insert carrier pilot
to GMSK using BBC coding and
highpass filter for coherent
demodulation is proposed. As an
illustrative example, the scheme
is applied to a 16Kbps BT=0.25
GMSK signal over a fast Rayleigh
fading channel with fD=100Hz,
and its performance is
investigated. The modem is found
to have an error floor of
Pe=5.5*10 -5 which is more than
one order of magnitude lower
than that of differential
detection. The effect of the
pilot recovery BPF on modem
performance is also
investigated. The optimum
bandwidth is found to be
fB=400Hz when the Doppler
frequency is 100Hz. Finally, the
effect of channel nonlinearity
on the signal spectrum is also
investigated. With the pilot
power 10dB below signal, the
amount of spectral spreading is
found to be minor for a certain
channel nonlinearity.
References:
[i] K. Murota, K. Hirade, "GMSK
modulation for digital mobile
radio telephony," IEEE Trans on
Comm. Vol. COM-29, No.7. ppi044-
1050, July 1981.
[2] J.R. Ball, "A real-time
fading simulator for mobile
radios," The Radio and
Electronic Eng., Voi.52, pp.475-
478, October 1982.
[3] A. Bateman, "A general
analysis of bit error
608
international Mobile Satellite Conference, Ottawa, _990
probability for reference based
BPSK mobile data transmission,"
IEEE Trans. on Comm. Vol. COM-
37, pp398-402, April 1989.
[4] R. Vaughan, "Signals in
mobile communications: A
review," IEEE Trans. on Veh.
Tech. Vol. VT-35, No.4. pp.133-
145, Nov.1986.
[5] F. Davarian, "Mobile digital
communications via Tone
Calibration," IEEE Trans. on
Veh. Tech. Vol. VT-36, pp.55-62,
May 1987.
[6] J. McGeehan, A. Batman,
"Phaselocked transparent tone-
in-band (TTIB): a new spectrum
of data over SSB mobile radio
networks," IEEE Trans. on Comm.
Vol. COM-32, pp.81-87, Jan.
1984.
[7] W. Rafferty, J.B. Anderson,
G.J. Saulnier, J.R. Holm,
"Laboratory measurements and a
theoretical analysis of the TCT
fading channel radio system,"
IEEE Trans. on Comm. Vol. COM-
35, pp172-180 Feb. 1987.
[8] I. Korn, "Coherent detection
of M-ary phase-shift keying in
the satellite mobile channel
with tone calibration," IEEE
Trans. on Comm. Vol. COM-37,
pp.997-i002 Oct. 1989.
[9] S. Gurunathan, K. Feher,
"Rayleigh fade compensated QPRS
coherent mobile radio modems
operated at a practical 2b/s/Hz
efficiency," IEEE Vehicular
Technology Conference, Orlando,
May 1990.
[I0] P.S.K. Leung, K. Feher
"Block-Inversion-Coded QAM
systems," IEEE Trans. on Comm.,
Voi.36, No.7, pp.797-805, July
1988.
[ii] J. Lodge, M. Moher, S.
Crozier, "A comparison of data
modulation techniques for land
mobile satellite channels," IEEE
Trans. on Veh. Tech. Vol. VT-36,
No.l, pp.28-35 Feb. 1987.
[12] P. Laurent, "Exact and
approximate construction of
digital phase modulations by
superposition of amplitude
modulated pulses (AMP)," IEEE
Trans. on Comm. Vol. COM-34,
No.2, pp.150-160, Feb. 1986.
[13] L.J. Greenstein, "Spectrum
of a binary signal block code
for DC suppression," BSTJ
VOI.53, No.6, pp. Ii03-i126,
July-Aug. 1974.
[14] H. Suzuki, Y. Yamao, H.
Kikuchi, "A single-chip MSK
coherent demodulation for mobile
radio transmission," IEEE Trans.
on Veh. Tech. Vol. VT-34 No.4.
pp.157-168, Nov. 1985
[15] K Hirade, "Mobile radio
communications," in K. Feher
"Advanced digital communicat-
ions, systems and signal
processing techniques,"
Prentice-hall, Englewood, 1987..
[16] M.K. Simon, C. Wang,
"Differential detection of
Gaussian MSK in a mobile radio
environment," IEEE Trans. on
Veh. Tech. Vol. VT-33, no4,
pp307-320, Nov 1984..
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711ter.
fc
Fiaure 1. Conceptual ceneratmn of GMSK slonal.
i
Floure 3a Transmitter of the GMSK modem w,th carder allot insertion.
Signalling pulse for GMSK.
BT=0.2
BT=O. 3
BTt0.5
BT=O0 (MSK).
-as o 05 |
FIourm 2. Slonalrino oulse alt_ for GMSK.
Figure 3b. Coherent detector of the coded GMSK modem.
P.S.D, of the BBC code.
='t2.e /_(a]
• (b) _-'/.
= {c} Y,,-I 1.
= _
o.
o 0.2 0.4
F,aure 4. Power _oectral density of BBC codes.
d
GMSK 9T=0.25 M=ll 8PF=4OOHZ NO F^OI_'G
o o
-1o t
-20
-1o I
-40 _!
-5o
-6o
-7o
-co [
-z
(e-tJ/t I
Fioure 5e. Soectmm of M = 11 BBC coded GMSK slanal with oiloL
fe = 400 Hz. No fad,co.
610
International Mobile Satellite Conference, Ottawa, t990
GMSK BT=0.25 M=ll BPF=4OOHZ FD=IOOHZ
-1o
-4o
i
-8o I.
It-Jr)/t ,
Figure 5b. SDeclrum of M = 11 BBC coded GMSK slanal with Dilot.
f. = 400 Hz. Fadin9 channel with fD =___
o o,
-_o
_[3 -3o
o
-4o
6
U_ -5o
-6o
Fiaure 5c.
_,,'ISK 8T=0.25 t'l=l[ BPF'=2OOHZ FD=IOOHZ
i
ii
-i o l
Soectrum of M - 11 RBC coded GMSK slonal w th [3ilot,
fe = 200 Hz Fatima channel with fD_= 100 Hz
I
-too
-ZOO
-_00
F_ure&
GMSKBT=0.25M=IIBBCcodedF =lOOHz.
(O) Ptl0t-elded Coherent det. fB-300H_
(b) Pilot-a(ded Coherent det, fB-4OONI
(¢) Otfferentt_t detection.
_........_ Ic)
I0 20 30 40 SO 60 c/N(,_).
Performance of M. 11 BBC coded GMSK modem in fast Ravleioh
tDdina channel. 16 kble. BT - 0.25. DooDler freauencv fo - 100 Hz,
Receive BPF bnndwldth, bit rate,
FIoure 7.
-2
-3 \
/
Error floor of M. 11 BBC coded GMSK slanal vs pilot recovery.
BPF bandwidth.
'_ o
f-.
-'o
-30
-4o
-'-,o
-lie
J v'l_
-I I i
(H=)le=
Rmmtrum of M. 11 RRC added GMRK rJonal with nJk_t.
fa" 400 Hz. Nonlinear channel wflh Io
International Mobile Satellite Conference, Ottawa, t990
6ti


A novel scheme to aid coherent detection of GMSK signals in fast Rayleigh fading channels

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